Randomized Kaczmarz (RK), Motzkin Method (MM) and Sampling Kaczmarz Motzkin (SKM) algorithms are commonly used iterative techniques for solving linear system of inequalities. As linear systems of equations represents a modeling paradigm for solving many optimization problems, these randomized and iterative techniques are gaining popularity among researchers in different domains. In this work, we propose a Generalized Sampling Kaczamrz Motzkin (GSKM) method that unifies the iterative methods into a single framework. In addition to the general framework, we propose a Nesterov type acceleration scheme in the SKM method called as Probably Accelerated Sampling Kaczamrz Motzkin (PASKM). We prove the convergence theorems for both GSKM and PASKM algorithms in the L2 norm perspective with respect to the proposed sampling distribution. Furthermore, from the convergence theorem of GSKM algorithm, we find the convergence results of several well known algorithms like Kaczmarz method, Motzkin method and SKM algorithm. We perform thorough numerical experiments using both randomly generated and real life (classification with support vector machine and Netlib LP) test instances to demonstrate the efficiency of the proposed methods. We compare the proposed algorithms with SKM, Interior Point Method (IPM) and Active Set Method (ASM) in terms of computation time and solution quality. In majority of the problem instances, the proposed generalized and accelerated algorithms significantly outperform the state-of-the-art methods.
The Sampling Kaczmarz-Motzkin (SKM) algorithm is a generalized method for solving large-scale linear system of inequalities. Having its root in the relaxation method of Agmon, Motzkin and the randomized Kaczmarz method, SKM outperforms the state-of-the-art methods in solving large-scale linear feasibility problems. Motivated by SKM’s success, in this work, we propose an Accelerated Sampling Kaczmarz-Motzkin (ASKM) algorithm which achieves better convergence compared to the standard SKM algorithm on ill conditioned problems. We provide a thorough convergence analysis for the proposed accelerated algorithm. We validate the convergence analysis with a set of numerical experiments on randomly generated linear system of inequalities.
The cost of pharmaceutical supply chain due to drug waste is one of the current major issues in health care. Drug waste associated with intravenous (IV) fluid form of medication is one of the crucial issues for many pharmacies. The purpose of this paper is to apply a cross-docking model to minimize the IV delivery lead time to reduce drug waste by scheduling staff in a local hospital’s inpatient pharmacy. A mixed integer linear programming model is applied to the IV delivery system of a hospital. The parameters are selected based on the observations made in the inpatient pharmacy. The result implies that cross-docking approach can be effectively applied to IV delivery system. In fact, the cross-docking optimization model employed in this case study reduces the IV delivery completion time of the inpatient pharmacy by 41 percent. The scope of this research is limited to the activities performed after IV preparation. The application of cross-docking system in staff scheduling will be beneficial for health care organizations that aim to minimize medication waste. The prime value of this study lies in the introduction of a cross-docking concept in an internal hospital ordering process. Cross-docking models are widely used in general supply chain systems; however, their application for specific activities inside hospitals is the novelty of this study, which can fill the research gap in terms of drug waste management within the inpatient pharmacy.
The growing healthcare industry is generating a large volume of useful data on patient demographics, treatment plans, payment, and insurance coverage—attracting the attention of clinicians and scientists alike. In recent years, a number of peer-reviewed articles have addressed different dimensions of data mining application in healthcare. However, the lack of a comprehensive and systematic narrative motivated us to construct a literature review on this topic. In this paper, we present a review of the literature on healthcare analytics using data mining and big data. Following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, we conducted a database search between 2005 and 2016. Critical elements of the selected studies—healthcare sub-areas, data mining techniques, types of analytics, data, and data sources—were extracted to provide a systematic view of development in this field and possible future directions. We found that the existing literature mostly examines analytics in clinical and administrative decision-making. Use of human-generated data is predominant considering the wide adoption of Electronic Medical Record in clinical care. However, analytics based on website and social media data has been increasing in recent years. Lack of prescriptive analytics in practice and integration of domain expert knowledge in the decision-making process emphasizes the necessity of future research.
Lack of efficiency and effectiveness of supply chain management systems in health care results in enormous cost for hospitals every year. One of the main critical elements of supply chain management in health care is pharmaceutical product ordering systems. Accuracy of demand estimation and agility of the delivery system are the main important factors in medication ordering systems in health care. Inadequacy of these two elements engenders a lot of waste for hospitals. Therefore, improving medical ordering systems results in significant benefit for pharmacies and hospitals. Respectively, utilization of lean tools (pull system) seems to be an effective way to improve agility of drug ordering systems as well as increase the accuracy of demand realization (push system). Thus, this research proposes to study the level of effectiveness of lean tool implementation for achieving the essential improvement in pharmaceutical product ordering systems. Following, a hypothetical case study is designed and the current medication ordering system is modeled using simulation software to generate yearly waste values; next, the drug ordering system is modified by implementation of Kanban system. Finally, the results of the modified model will be compared with the results of the initial system and optimized push system.